Photon tunneling gated by light at a different wavelength in an artificially created array of nanometer scale cylindrical channels in a thick gold film is described. This observation suggests the possibility of buildi...
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Dynamical systems with chaos on an invariant submanifold can exhibit a type of behavior called bubbling, whereby a small random or fixed perturbation to the system induces intermittent bursting. The bifurcation to bub...
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Dynamical systems with chaos on an invariant submanifold can exhibit a type of behavior called bubbling, whereby a small random or fixed perturbation to the system induces intermittent bursting. The bifurcation to bubbling occurs when a periodic orbit embedded in the chaotic attractor in the invariant manifold becomes unstable to perturbations transverse to the invariant manifold. Generically the periodic orbit can become transversely unstable through a pitchfork, transcritical, period-doubling, or Hopf bifurcation. In this paper a unified treatment of the four types of bubbling bifurcation is presented. Conditions are obtained determining whether the transition to bubbling is soft or hard; that is, whether the maximum burst amplitude varies continuously or discontinuously with variation of the parameter through its critical value. For soft bubbling transitions, the scaling of the maximum burst amplitude with the parameter is derived. For both hard and soft transitions the scaling of the average interburst time with the bifurcation parameter is deduced. Both random (noise) and fixed (mismatch) perturbations are considered. Results of numerical experiments testing our theoretical predictions are presented.
We present a systematic method for the design of tunable directional couplers and arrayed waveguide couplers in photonic crystals. Two methods for controlling the coupling length are proposed. Bending of coupled waveg...
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We study the statistics and characteristics of rare intense events in two types of two-dimensional complex Ginzburg-Landau (CGL) equation based models. Our numerical simulations show finite amplitude collapselike solu...
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We study the statistics and characteristics of rare intense events in two types of two-dimensional complex Ginzburg-Landau (CGL) equation based models. Our numerical simulations show finite amplitude collapselike solutions which approach the infinite amplitude solutions of the nonlinear Schrödinger equation in an appropriate parameter regime. We also determine the probability distribution function of the amplitude of the CGL solutions, which is found to have enhanced (as compared to Gaussian) probability for the amplitude to be large. Our results suggest a general picture in which an incoherent background of weakly interacting waves, occasionally, “by chance,” initiates intense, coherent, self-reinforcing, highly nonlinear events.
Polarization effects in surface plasmon polaritonic crystals (two-dimensional photonic crystals on a metal surface) are observed in the optical transmission of metallic nanostructures and the directional switching bet...
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We consider the long time dependence for the moments of displacement 〈|r|q〉 of infinite horizon billiards, given a bounded initial distribution of particles. For a variety of billiard models we find 〈|r|q〉∼tγq (...
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We consider the long time dependence for the moments of displacement 〈|r|q〉 of infinite horizon billiards, given a bounded initial distribution of particles. For a variety of billiard models we find 〈|r|q〉∼tγq (up to factors of lnt). The time exponent, γq, is piecewise linear and equal to q/2 for q<2 and q−1 for q>2. We discuss the lack of dependence of this result on the initial distribution of particles and resolve apparent discrepancies between this time dependence and a prior result. The lack of dependence on initial distribution follows from a remarkable scaling result that we obtain for the time evolution of the distribution function of the angle of a particle’s velocity vector.
Photon tunneling gated by light at a different wavelength in an artificially created array of nanometer scale cylindrical channels in a thick gold film is described. This observation suggests the possibility of buildi...
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Photon tunneling gated by light at a different wavelength in an artificially created array of nanometer scale cylindrical channels in a thick gold film is described. This observation suggests the possibility of building a new class of "gated" photon tunneling devices for massive parallel all-optical signal and image processing.
In this paper, we present the experimental cold-test results of the new input cavity and the hot tests of this new 4 cavity, frequency-doubling coaxial gyroklystron. The input cavity was redesigned to have a lower qua...
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In this paper, we present the experimental cold-test results of the new input cavity and the hot tests of this new 4 cavity, frequency-doubling coaxial gyroklystron. The input cavity was redesigned to have a lower quality factor and located the lossy absorbers inside the cavity structure, rather than in the adjacent drift tube sections. The average radius of the cavity was increased to make that cavity less susceptible to spurious oscillations. The designed 4 cavity frequency doubling system have a high large signal gain above 50 dB.
Simultaneous perturbation stochastic approximation (SPSA) algorithms have been found to be very effective for high-dimensional simulation optimization problems. The main idea is to estimate the gradient using simulati...
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Simultaneous perturbation stochastic approximation (SPSA) algorithms have been found to be very effective for high-dimensional simulation optimization problems. The main idea is to estimate the gradient using simulation output performance measures at only two settings of the N -dimensional parameter vector being optimized rather than at the N + 1 or 2N settings required by the usual one-sided or symmetric difference estimates, respectively. The two settings of the parameter vector are obtained by simultaneously changing the parameter vector in each component direction using random perturbations. In this article, in order to enhance the convergence of these algorithms, we consider deterministic sequences of perturbations for two-timescale SPSA algorithms. Two constructions for the perturbation sequences are considered: complete lexicographical cycles and much shorter sequences based on normalized Hadamard matrices. Recently, one-simulation versions of SPSA have been proposed, and we also investigate these algorithms using deterministic sequences. Rigorous convergence analyses for all proposed algorithms are presented in detail. Extensive numerical experiments on a network of M/G/1 queues with feedback indicate that the deterministic sequence SPSA algorithms perform significantly better than the corresponding randomized algorithms.
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